Understanding Power using Kirchhoff’s Rules
Subject Area(s)
Physics
Associated Unit
Lesson Title
None
Understanding Power using Kirchhoff’s Rules
Grade Level
12
Lesson #
1 of 1
Time Required
2 classes
Summary
The idea of this lesson is to show how Kirchhoff’s Rules are used in real
world applications in the power delivery system. This lesson is a great
review of many of the concepts for the second semester of AP Physics C,
Electricity and Magnetism.
Engineering Category
Electrical Engineering
Keywords
Phase Power, Kirchhoff’s Rules, Transformers
Educational Standards
AP Physics C standards
http://www.collegeboard.com/student/testing/ap/physics_c/topics.html#newtMech
Pre-Requisite Knowledge
Students must understand series and parallel circuits, Ohm’s law and
power.
Learning Objectives

The student will understand the differences between one phase, split
phase, and three phase power.

The student will be able to calculate current, power or voltage using
Kirchhoff’s rules and Ohm’s law for complex circuits.

The student will be able to calculate the various component parts of a
transformer.
Introduction / Motivation
If you want to buy a new tool or appliance, how do you know if you want
to buy a 120V or 240V device? Why does it matter?
Lesson Background & Concepts for Teachers
www.allaboutcircuits.com is a web site with a plethora of information.
Additionally, the Power Point presentation would be helpful to preview
prior to beginning the lesson. MIT also has an open courseware where
you can download information. The link here is for the E&M course video
files: http://ocw.mit.edu/OcwWeb/Physics/8-02Electricity-andMagnetismSpring2002/VideoAndCaptions/index.htm.
Vocabulary / Definitions
Word
Definition
Transformer An electric device consisting essentially of two or more windings wound on the
same core, which by electromagnetic induction transforms electric energy from
one set of one or more circuits to another set of one or more circuits such that
the frequency of the energy remains unchanged while the voltage and current
usually change.
Single
A circuit having an alternating current with one phase or with phases differing by
phase
180°.
Split Phase A current in one of two parallel circuits that have a single-phase current source
but unequal impedances and that produce currents of different phase.
Three
A circuit, system, or device that is energized by three electromotive forces that
Phase
differ in phase by one third of a cycle or 120°.
Inductance
Property of a circuit by which a change in current induces, by electromagnetic
induction, an electromotive force.
Magnetic
A measure of the quantity of magnetism, being the total number of magnetic
Flux
lines of force passing through a specified area in a magnetic field.
Coil
A conductor, as a copper wire, wound up in a spiral or other form.
Lesson:
Go over the material in the presentation Power and Kirchhoff.
Have an electrical engineer or a representative from the local power
company visit with the class.
Go over example problems and assign additional problems.
Problems on student worksheet utilized from the following resources:
Beiser, Arthur. Theory and Problems of Applied Physics. 3rd. New York: McGraw-Hill, Inc., 1995.
Print.
Tipler, Paul. Physics for Scientists and Engineers. 4th. New York: W.H. Freeman and Company,
1999. Print.
AP Physics Student WS – Power and Kirchhoff
Direct Current using Kirchhoff’s Rules
b
R2 = 5.00
a
ε1 = 12.00 V
r1=1.00 Ω
c
ε2 = 4.00 V
r2=1.00 Ω
Example 1:
Find the potentials at points a through e.
Note that r1 and r2 denote internal resistance of
the batteries. Assume the potential at point e is
zero.
Discuss the energy transfers in the circuit.
R1 = 5.00 Ω
e
d
R3 = 4.00 Ω
Problem 1:
Find the current in each branch of the circuit. Find the energy dissipated in the 4.0 Ω resistor in
3.0 seconds.
12.0 V
2.0 Ω
4.0 Ω
5.0 V
3.0 Ω
Transformers:
Example 2:
To verify the advantage of using high voltage transmission lines, find the rate of energy loss due
to heat when a 5 Ω cable is used to transmit 1 kW of electricity at 100 V and again at 100,000 V
(100kV).
Problem 2:
The transformer in an electric welding machine draws 3A from a 240 V ac power line and
delivers 400 A of current. What is the potential difference across the secondary coil of the
transformer?
Problem 3:
A 240 V, 400 W electric mixer is connected to a 120 V power line through a transformer. What
is the ratio of turns in the transformer? How much current is drawn from the transmission line?
R-L-C Circuits
10.0 Ω
2.0 mH
80.0 µF
10.0 V
1000. Hz
Example 3:
Find the current in each component of the R-L-C circuit.
Find the total current in the circuit. Find the impedance of the circuit. Find the phase angle and
the total power dissipation of the circuit.
Problem 4:
A 60 µF capacitor, a 0.3 H inductor, and a 50 Ω resistor are connected in series with a 120 V, 60
Hz power source. Find the impedance of the circuit, the current in the circuit, the power it
dissipates, and the minimum rating in volt-amperes of the power source.
Lesson Closure
The students will write a brief technical report on the pros and cons of
buying a device for 120V or 240V power.
Assessment
Grade additional homework problems and student generated report.
Other
Cultural relevance is covered in this lesson plan by bringing in a
representative from the local power company or an electrical engineer.
Creator
Danielle Reynolds / Duncanville High School
Sponsor
University of Texas at Arlington / Electrical Engineering
National Science Foundation under Grant No. EEC-0808687